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Answer 1

$\huge\boxed{\green{Question\: 11 :-}}$

$\large\underline\mathbf\blue{Given :-}$

$\small\implies\mathbf{⊖ = 30°}$

$\large\underline\mathbf\green{To\: Find:-}$

$\small\implies\mathbf{The\:value\:of\::-}\\{\frac{5sin⊖}{3-2cos⊖}}$

$\large\underline\mathbf\red{Solution :-}$

$\small\mathbf{If\:⊖=30°\: then,}\\{\mathbf{†\:we\:know\:sin\:30°=\frac{1}{2}}}$

$\small\mathbf{Thus,\: Perpendicular=1\:units}\\{\mathbf{ Hypotenuse=2\:units}}$

$\small\implies\mathbf{Then,\:by\: Pythagoras\: theorem:-}$

$\small\mathbf{†\:Hypotenuse²=(Base)²+(Perpendicular)²}$

$\small\implies\mathbf{Base²=4-1}$

$\small\therefore\mathbf\red{Base=√3}$

$\small\implies\mathbf{Now,}$

$\small\implies\mathbf{5sin⊖=5×\frac{1}{2}=2.5}$

$\small\implies\mathbf{3-2cos⊖=3-(2×\frac{√3}{2})=3-√3}$

$\small\mathbf{†\:Lastly,\:Putting\:the\:values,}$

$\small\implies\mathbf{\frac{5sin⊖}{3-cos⊖}}$

$\small\implies\mathbf{\frac{2.5}{3-√3}}$

$\large\boxed{\red{∴\frac{5sin⊖}{3-cos⊖}=\frac{2.5}{3-√3}}}$

$\huge\boxed{\purple{Question\:12:-}}$

$\small\implies\mathbf{As\:we\:know,}\\{\implies\mathbf{⊖=30°,then :-}}$

$\small\implies\mathbf{[sin30°×cos(90-30°)]+}\\{\mathbf{[cos30°×sin(90°-30°)]}}$

$\small\implies\mathbf{(sin30°×cos60°)+(cos30°×sin60°)}$

$\small\implies\mathbf\red{we\:know\:that:-}$

$\small\mathbf{•\:sin30°=\frac{1}{2}}$

$\small\mathbf{•\:sin60°=\frac{√3}{2}}$

$\small\mathbf{•\:cos30°=\frac{√3}{2}}$

$\small\mathbf{•\:cos60°=\frac{1}{2}}$

$\small\therefore\mathbf\blue{Applying\:the\:values:-}$

$\small\implies\mathbf{(\frac{1}{2}×\frac{1}{2})+(\frac{√3}{2}×\frac{√3}{2})}$

$\small\implies\mathbf{\frac{1}{4}+\frac{3}{4}}$

$\small\implies\mathbf{\frac{4}{4}=1}$

$\small\boxed{\red{\mathbf{∴(sin⊖×cos(90-⊖)+(cos⊖×sin(90-⊖) = 1}}}$